Developmental changes in straight gait in childhood

Background Understanding typical gait development is critical in developing suitable physical therapy methods for gait disorders. This study investigated the developmental changes and controlling mechanisms of straight gait. Methods We conducted an experimental procedure among 90 participants, including 76 typically developing children and 14 healthy adults. The children were divided according to age into 3–4, 5–6, 7–8, and 9-10-year age groups. We created two indices to quantify straight gait using the extrapolated center of mass (XCOM; goal index, XCOMG and actual progress index, XCOMP), which were calculated and compared between the groups. Stepwise multiple regression was used to examine the effects of each gait variable on XCOMG and XCOMP. To eliminate the effects of multicollinearity, correlation coefficients were calculated for all gait variables. Results Both XCOMG and XCOMP decreased gradually with age and were significantly larger in the 3–4 and 5–6 year groups than in the adult group. Multiple regression analysis showed that step velocity, step width, and the coefficiente of variation (CV) of the step width had independent coefficients of variation for the XCOMG, and the symmetry index of step time, step width, and the CV of the step width had independent CV for the XCOMP. These variables were selected as significant variables. The results showed that meandering gait was more pronounced at younger ages. Furthermore, straight gait observed in adulthood was achieved by the age of 7. Conclusion Pace (step velocity) and stability (step width and CV of step width) may contribute to XCOMG, which assesses the ability to proceed in the direction of the target. Stability and symmetry may contribute to XCOMP, which assesses the ability to walk straight in one’s own direction of progress. Physical therapists could apply these indices in children to assess their ability to walk straight.

Introduction Neurodevelopmental disorders such as developmental coordination disorder (DCD) impair gait and postural control. The parents of children with DCD and other developmental disorders often complain that their children cannot walk straight. A previous study focusing on the gait ability of children with DCD at ages 7-12 (young children) and ages 12-17 (older children) showed that the younger the child, the greater the variation in the body's center of mass (COM) velocity and antero-posterior and lateral acceleration [1]. Additionally, children with attention deficit hyperactivity disorder have been reported to have greater variability in speed, cadence, and stride length [2]. In children with neurodevelopmental disorders, the inability to walk straight and the tendency to fall are related to postural control in immature walking. However, no studies have examined the relationship between the ability to walk straight and postural control. This is primarily because no studies have examined when and how meandering gait develops into a straight gait in childhood. To develop appropriate physical therapy for gait disorders, it is important to understand various aspects of typical gait development [3]. To the best of our knowledge, straight gait has not been clearly identified; therefore, it may be defined by various values regarding the trajectory of the center of mass (COM) and/or foot position [4]. Vertical and mediolateral fluctuations of the COM while walking are larger in those aged �4 years than in adults, and are larger in the anteroposterior direction at age �7 years [5]. Based on these results, the stability of COM control during walking was reported to improve up to the age of 7 years [5]. Recently, the extrapolated center of mass (XCOM) based on an inverted pendulum model has been used to assess stability during dynamic tasks such as walking [6]. This variable takes both the deviation and velocity of the COM into consideration. Thus, XCOM can indicate an index of stability, and may be linked to gait straightness. Stability has previously been characterized as the displacement of XCOM from the direction of travel during one gait cycle [7]. XCOM along the mediolateral axis was reported to have a strong negative correlation with ages 1-11 years, which is linked to changes in the step time-distance parameters of gait [7]. Although there is no clear definition of straight gait, to evaluate the straightness of the gait, the deviation from the straight line connecting the start to the target needs to be evaluated in addition to the displacement from the participant's actual direction of travel. Therefore, we devised two indices to quantify the ability to walk straight using XCOM: 1) deviation from the intended direction (G index) and 2) body sway with respect to the direction of progress (P index). The G index evaluates the ability to move straight toward the target; thus, smaller values are thought to reflect a better ability to capture the target and appropriately control the gait in the direction of the target. A smaller P index is thought to reflect appropriately control of the body sway in the direction of progress. Previous studies using the G index have not been reported. We created the G index with the expectation that it can be a new index for evaluating gait and postural control while an individual walks towards a goal.
Mani et al. [8] clarified the developmental process of gait in childhood using the five functional domains of the gait variables reported by Lord et al. [9]. They examined 189 elderly people with steady gaits to classify 16 gait variables into five functional domains using principal component analysis. These domains were pace (step length, step time, and swing time standard deviation [SD]), rhythm (step time, stance time, and swing time), asymmetry (left-right asymmetry of step time, stance time, and swing time), variability (step length SD, step velocity SD, step time SD, and stance time SD), and postural control (step width, step width SD, and mediolateral asymmetry of step length) [8]. Mani et al. reported that pace, rhythm, and asymmetry developed relatively quickly, reaching adult levels around the age of 7 years, while variability and postural control were still not mature by age 10 years. Examining the relationships between these five gait functional domains and the straight gait indices could help us understand what kind of control functions are required to walk straight.
Therefore, the purpose of the present study was to clarify the developmental changes in straight gait and the control mechanisms involved. We hypothesized that: (1) gait becomes more straight with age and reaches the adult level after the age of 7 years [5]; (2) functional domains of the gait stability, such as asymmetry and postural control, are associated with the ability to perform straight gait, and, the G index and P index are associated with different control functions.

Subjects
Ninety subjects, including 76 typically developing children (age 3-10 years) and 14 healthy adults participated in this study. The children were divided into a 3-4 (n = 25), 5-6 (n = 25), 7-8 (n = 14), and 9-10 year age groups (n = 12). Table 1 shows the physical characteristics of each group. The inclusion criteria were typical gross motor development (based on the developmental history of the child obtained from the guardian), the ability to understand an explanation of the experiment, and the ability to walk independently. The exclusion criteria were a history of orthopedic surgery or neurological disease. The study's objective, experimental procedure, and possible risks were fully explained to the subjects and their guardians in advance, both verbally and in writing, and written consent was obtained from the guardians. This study was approved by the ethical review boards of Sapporo Medical University and the Oita University Faculty of Welfare and Health Sciences (approval nos. 28-2-52, F200016).

Experimental procedures and tasks
The subject was instructed to walk barefoot at a comfortable speed on a straight walking path toward a research assistant (who encouraged them forward) 6 m away. The walking path was created with a length of 4m and a width of 1.5m (Fig 1). The instructions were very simple:

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"Please walk straight towards me." In some cases, parents gave instructions for younger children who could not follow the instructions of research assistants. Parents or research assistants stood behind video camera positioned at 1m away from end point, defined as the edge of walking path (Fig 1). Kinematic data were recorded during walking with a 10-camera VICON Nexus 3D motion analysis system (VICON, MX, USA). The sampling frequency was 100 Hz. A total of 27 infrared reflective markers 9.5 mm in diameter were fixed to the skin on the body and bone landmarks. The arrangement of the markers followed the method of Jensen [10] to calculate body-skeletal characteristics from physical measurement data. To eliminate the influence of acceleration and deceleration at the start and end of walking, we recorded the middle 4 m of the kinematic data. The start was always from the same position at 1m before from the edge of walking path (Fig 1). After practicing the task several times, the results were recorded five times. The mean value of these data was used for analysis. To eliminate the influence of fatigue, short breaks were taken at the subject's discretion, or after every two tasks. The length of the leg was defined as the distance from the greater trochanter to the floor.

Data analysis
All signals were processed offline using MATLAB R2020b (MathWorks, Natick, MA, USA). The 3D data were processed using a Butterworth fourth-order low-pass filter (cutoff frequency, 20 Hz). The analysis range for defining straight gait was 2 m, which was the maximum range over which all marker data for all participants could be recorded without missing data. At least two gait cycles were recorded per trial for all the subjects. Heel contact (HC) was defined as the time when the vertical coordinate of the calcaneal marker was at its minimum. The first HC was HC1st. COM was calculated using the body skeletal data from Jensen et al. [10]. In addition, XCOM was calculated using the equation of Hof et al. (Eq 1) [6], as follows: where x is the COM position, v is the velocity of the COM, g is the gravitational acceleration, and l is the distance from the external malleolus marker to the COM. Straight gait was quantified using the two methods (Fig 2). The G index was calculated using the XCOM coordinate at HC1st as the origin and was the integral of the deviation between the goal axis toward the end point, and the XCOM coordinate (XCOM G ). The larger this variable, the greater the deviation of the trajectory of the body from the axis from start to the goal. For the actual progressive index (P index), a straight line connecting the XCOM coordinates at HC1st and the XCOM coordinates at 2 m was defined as the progress axis. This was used to calculate the integral of the deviation between the progress axis and the XCOM coordinate (XCOM P ). The larger this variable was, the greater the postural sway with respect to the direction of travel, indicating less stability. These variables were normalized to the height of the COM [11].
Each gait variable was calculated using bilateral calcaneal markers and second metatarsal head markers. Foot off (FO) was defined as the time when the second metatarsal head marker exceeded 5% from the minimum to the maximum height.
Step length (SL) was the anteroposterior distance between the heels from the HC on one side to the HC on the other side. The step width (SW) was defined as the distance between the heel markers on a perpendicular line connecting the directions of progress of each side.
Step time (ST) was the time from the HC of one leg to the HC of the opposite leg.
Step velocity (SV) was calculated by dividing SL by the step time. Stance time (STT) was defined as the time from the HC of one leg to the FO of the

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Developmental changes in straight gait in childhood same leg. Swing time (SWGT) was the time from the FO of one leg to the HC of the same leg. The means of the left and right steps were used as the representative values. For SD, the mean of the variance of the left and right steps was calculated (Eq 2) [12,13]. Lord et al. [13] used SD as a variable indicating variability, and the absolute values of the differences between each step were used as variables of left-right symmetry. However, because SD depends on the mean, the coefficient of variation (CV) is more suitable for analyzing variability. Moreover, the symmetry index (SI) has been shown to be a highly valid index of symmetry [14,15]. Therefore, in the present study, CV and SI were calculated as follows (Eq 3): SD ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi variance of left step þ variance of right step 2 Distance variables such as SL and SW were normalized by dividing them by leg length (L), SV by ( p gL), and time variables by the equation ( p (L/g)) [16,17], where g indicates gravitational acceleration.
For the statistical analysis, all variables were normally distributed based on the Shapiro-Wilk test and the shape of the distributions with histograms. We performed a regression analysis to examine whether age affects XCOM G and XCOM P in typically developing children. ANOVA was used to compare the adult and child age groups, and the Tukey method was used for multiple comparisons. To examine the effects of velocity, as with SV, ANOVA was used to compare the adult and child age groups. Stepwise multiple regression was used to examine the effects of each gait variable on XCOM G and XCOM P . To eliminate the effects of multicollinearity, correlation coefficients were calculated for all the gait variables. For variables with strong correlations (r � |0.7|), one was excluded from the analysis. Eight variables were used in the multiple regression analysis: pace: SL, SV; rhythm: ST; symmetry: ST_SI; variability: SL_CV, SV_CV; and stability: SW, SW_CV. The significance level was 0.05.

Development of straight gait in childhood
Both XCOM G and XCOM P gradually decrease with age, and after the age of 7, the ability became equivalent to that of adults. Table 2 shows the results of the regression analyses of age with XCOM G and XCOM P . Both XCOM G and XCOM P decreased significantly with development (R 2 = 0.22, R 2 = 0.18, p < 0.01) (Fig 3A and 3B). Table 3 shows the mean values and SD for the XCOM G , XCOM P , and SV for the groups. XCOM G and XCOM P were both significantly different between the groups (XCOM G : F 4,88 = 11.85, p < 0.01; XCOM P : F 4,88 = 14.14, p < 0.01). The multiple comparison results showed that both XCOM G and XCOM P were significantly larger in the 3-4 and 5-6 year age groups than in adults. SV was not significantly different between the groups (F 4,88 = 1.57, p = 0.19).   Table 4 shows the multiple regression results of XCOM G and XCOM P for each gait variable.

Development of straight gait in childhood
Overall, our results supported our first hypothesis; both the XCOM G and XCOM P scores decreased significantly with increasing age in children aged 3-10 years. Furthermore, comparison of the indices between adult and various age groups revealed that the adult level was reached at the age of 7 years. This result supports that of Dierick et al. [5], who found that stability improves up to the age of 7 years. The central nervous system controls posture during walking via complex processing that integrates input from the vestibular, visual, and somatic sensations [18]. Sensory information processing improves with development [19]. In childhood, when connectivity at the cortical-spinal level is immature, control via the spinal cordbrainstem is thought to contribute to the control of gross movements [20,21]. The central pattern generators (CPGs) associated with locomotion contribute to adjusting the motion patterns and rhythms of the limbs during walking [21]. Afferent information from the skin strongly affects CPGs [20], and somatic sensory function has been shown to reach an adult level at the age of 3-4 years [19]. This suggests that domains that express gait patterns, such as step, time factors, and left-right symmetry, are associated with corrections at the spinal cordbrain stem level, or CPGs, and are acquired relatively early (by about 7 years of age). Compared to the that of the adult group, the XCOM G and XCOM p results did not show statistically significant differences between the 7-8 years old and 9-10 years old groups in this study. Therefore, the development of straight gait continues until the age of 7 years, when a certain degree of gait control and various forms of posture control have been acquired. Although not significantly different, the two groups tended to have higher values than the adults, which may indicate that they develop gradually even after the age of seven.

Control mechanisms involved in straight gait
Here, two indices were devised to capture meandering gait: 1) deviation from the direction toward the target (G index); and 2) body sway with respect to the direction of progress (P index). The G and P indices were found to be associated with different functional gait domains, supporting our second hypothesis. XCOM G evaluates the ability to go straight toward the target, and in addition to stability, it reflects the ability to accurately focus on the target and control the gait appropriately in that direction. Thus, this index expresses one component of the ability to walk straight. The XCOM G was significantly higher in the the 3-4 years old and 5-6 years old groups compared to that of the adult group. Therefore, the present results suggest that the ability to accurately focus on the target and control the gait appropriately in a particular direction reaches an adultlike level at age 7-8.
The results of this study indicate that SV, SW, and SW_CV contribute to XCOM G (Table 4). SV is classified under pace in the five functional gait domains. Because the present study used variables normalized by the height of COM, it eliminated the effects of physique, and thus likely reflects the growth of the parts of the nervous system involved in the basic control of walking [17]. Moreover, a correlation was observed between the SW and SW_CV. Both of these are classified as 'stability' in the five functional gait domains [8,9]. This indicates that the goal index is not only associated with the control mechanism of stability, but also with the basic mechanism for adjusting gait (pace). However, in a previous study, the authors found that SW in children aged 3-4 years was not significantly different from that in adults, though SW_CV in children up to the age of 9 or 10 years was significantly different from that in adults [9]. This suggests that the variable contributing to stability requires a high level of control that is not mature even by the age of 10 years [9]. Gait stability requires controlling purposeful motions through predictive adjustment and constantly integrating various forms of sensory information generated during motion [18]. It has been suggested that this continues to develop even after the age of 10 years [9]. These results suggest that XCOM G is associated with SV, which is classified under pace, and with SW and SW_CV, which are classified under stability, and decreases gradually over time to accompany the growth of basic mechanisms for adjusting gait and the development of gait stability.
The multiple regression analysis conducted in this study indicated that ST_SI, SW, and SW_CV are involved in XCOM P . Interestingly, unlike the G index, the P index was not only associated with stability functions, but also with ST_SI or symmetry functions. Left-right differences in spatiotemporal gait variables affect the deviation of COM during walking [22]. However, symmetry develops relatively early, reportedly reaching adult levels around the age of 3-4 years [9]. In contrast, SI variability is greater at younger ages [9]. XCOM P is designed to evaluate whether a person can maintain a straight line in the direction of intended progress, that is, the ability to appropriately control body sway. Therefore, the development of stability control to limit body sway and left-right symmetry control as it relates to stability are important to XCOM P .

Limitations
This study has several limitations which should be mentioned. First, we did not take sex differences into account, although prior research has found that sex influences postural control during walking [23]. Jensen et al.'s data [10], which we used in the analysis of COM, are body measurements from boys aged 4-15 years. The subjects of the present study included children as young as 3 years old and girls of various ages, which may have influenced the results. Secondly, we could not sufficiently examine data validity. There are no previous studies that investigated meandering gait; thus, we could not examine criterion-related validity. Moreover, the use of the XCOM measures for a whole trial (multiple gait cycles) as opposed to within step were different slightly to those stated by Hof et al. [6] and Hallemans et al. [7]. However, XCOM is a widely used analytical method, and we believe that because of its strong association with stability, it will not have a major impact on the conclusions of this study of novel indices. As such, more valuable results may be obtained by increasing the number of subjects and examining sex differences and validity.

Conclusion
In this study, we devised two indices for straight gait and analyzed the developmental process in boys and girls aged 3-10 years. Stability and pace may contribute to the goal index, which assesses the ability to proceed in the direction of the target. Stability and symmetry may contribute to the ability to walk straight in one's own direction of progress, even if it is skewed. The two indices presented in this study are effective parameters for evaluating meandering and postural stability during gait. Kozuka.